use Lemon::Graph;

# read graph from file with a cost map encoding arc lengths
my $graph = Lemon::GraphReader->new("some_graph.lgf")->
    arcMap("cost", my $cost)->
    run();

my $source = ... some node ...;
my $destination = ... some other node ...;

# create a shortest path object
my $d = Lemon::Dijkstra->new($graph, $cost);

# run Dijkstra from $source
$d->run($source);

# get the distance to $destination
my $dist = $d->dist($destination);